behavioral econ

3- Suppose A is the set of positive real numbers, and suppose u and v are two strictly increasing functions. It is intuitive that u and v are ordinally equivalent, since both rank larger numbers higher, and therefore generate the same ranking of numbers. Write this intuition as a proof. 4- (i) Formally define the notion that "choice data is consistent with util- ity maximization". (Hint: take inspiration from the definition of "consistency with preference maximization" ). (ii) Supposing that A is finite, prove that choice data is consistent with utility maximization if and only if it satisfies WARP. (Hint: string together propositions in the lecture notes)